The following is from: Light and Color, by Clarence Rainwater, Prof. of Physics, San Francisco State College, Original Project Editor Herbert S. Zim, Golden Press, NY, Western Publishing Company, Inc., 1971.

Laws of Refraction.
1. Incident and refracted rays lie in the same plane.

2. When a ray of light passes at an angle into a denser medium, it is bent toward the normal, hence the angle of refraction (r) is smaller than the angle of incidence (i)...

3. The index of refraction of any medium is the ratio between the speed of light in a vacuum (or in air) and its speed in the medium. [pg. 43]

The Index of Refraction [n] determines the amount of bending of a light ray as it crosses the boundary from air into the medium. [pg. 43]

Internal Reflection occurs whenever a light ray strikes the surface of a medium whose refractive index is less than that of the medium in which the light is traveling. The amount of light that is reflected depends on the angle at which it hits the surface. Light from a point source (above) hits the surface at many angles. [pg. 44]

Dispersion is the separation of light into its component wavelengths. One method of dispersing a light beam is to pass it through a glass prism--a thick piece of glass with flat non-parallel sides (below). The refractive index of all materials depends slightly on the wavelength of the light. For glass and other transparent materials the refractive index is larger for the short (blue) wavelengths than for the longer (red) ones. Thus, when a beam of white light is passed though a prism, the blue rays will be bent more than the red rays--that is, the light spreads out to form a spectrum. The colors in the spectrum appear in the order of increasing wavelength: violet, blue, green, yellow, orange, and red. Sir Isaac Newton first explained the spectrum. He showed that, contrary to popular belief, the prism did not create the beautiful colors, but only made visible the components of white light.

Scientists make use of dispersion in the analysis of light emitted or absorbed by various materials both on the earth and on other bodies in space.[pg. 45]

Diffraction is the bending of waves around an obstacle. It is easy to see this effect for water waves. They bend around the corner of a sea wall, or spread as they move out of a channel. Diffraction of light waves, however, is harder to observe. In fact, diffraction of light waves is so slight that it escaped notice for a long time. The amount of bending is proportional to the size of light waves--about one fifty-thousandth of an inch (5,000 A)--so the bending is always very small indeed.

When light from a distant street lamp is viewed through a window screen it forms a cross. The four sides of each tiny screen hole act as the sides of a slit and bend light in four directions, producing a cross made of four prongs of light. Another way to see the diffraction of light waves is to look at a distant light bulb through a very narrow vertical slit. Light from the bulb bends at both edges of the slit and appears to spread out sideways, forming an elongated diffraction pattern in a direction perpendicular to the slit.

Light can be imagined as waves whose fronts spread out in expanding concentric spheres around a source. Each point on a wave front can be thought of as the source of a new disturbance. Each point can act as a new light source with a new series of concentric wave fronts expanding outward from it. Points are infinitely numerous on the surface of a wave front as it crosses an opening.

As new wave fronts fan out from each point of a small opening, such as a pinhole or a narrow slit, they reinforce each other when they are in phase and conceal each other when they are completely out of phase. Thus lighter and darker areas form the banded diffraction patterns.... Diffraction patterns are formed when light passes through pinholes and sits. A pinhole gives a circular pattern and a slit gives and elongated pattern. A sharper image is not formed by light passing through because of diffraction. As the pinhole or slit gets smaller, the diffraction pattern gets larger but dimmer. In the diffraction patterns shown below the alternate light and dark spaces are due to interference between waves arriving from different parts of the pinhole or slit. [p. 46-47]

Interference is an effect that occurs when two waves of equal frequency are superimposed. This often happens when light rays from a single source travel by different paths to the same point. If, at the point of meeting, the two waves are in phase (vibrating in unison, and the crest of one coinciding with the crest of the other), they will combine to form a new wave of the same frequency. The amplitude of the new wave is the sum of the amplitudes of the original waves. The process of forming this new wave is called constructive interference.

If the two waves meet out of phase (crest of one coinciding with a trough of the other), the result is a wave whose amplitude is the difference of the original amplitudes. This process is called destructive interference. If the original waves have equal amplitudes, they may completely destroy each other, leaving no wave at all. Constructive interference results in a bright spot; destructive interference produces a dark spot.

Partial constructive or destructive interference results whenever the waves have an intermediate phase relationship. Interference of waves does not create or destroy light energy, but merely redistributes it.

Two waves interfere only if their phase relationship does not change. They are than said to be coherent. Light waves from two different sources do not interfere because radiations from different atoms are constantly changing their phase relationships. They are non-coherent (see lasers....). [pg. 48-49]

Iridescent colors, which change the appearance with the angle of viewing and the direction of the illumination, are due to interference. The delicate hues of soap bubbles and oil films, the pale tints of mother-of-pearl, and the brilliant colors of a peacock's tail are all iridescent colors..... A soap bubble appears iridescent under white light when the thickness of the bubble is of the order of a wavelength of light. This occurs because light waves reflected from front and back surfaces of the film travel different distances. A difference in phase results that may cause destructive interference for some particular wavelength, and the hue or color associated with that wavelength will be absent from the reflected light. If the missing hue is red, reflected light appears blue-green, the complement of red. If film thickness or direction of illumination changes, interference occurs at different wavelengths and the reflected light changes color. [pg. 49]

Scattering is the random deflection of light rays by fine particles. When sunlight enters through a crack, scattering by dust particles in the air makes the shaft of light visible. Haze is a result of light scattering by fog and smoke particles.

Reflection, diffraction, and interference all play a part in the complex phenomenon of scattering. If the scattering particles are of uniform size and much smaller than the wavelength of light, selective scattering may occur and the material will appear colored, as shown above. Shorter wavelengths will be scattered much more strongly than longer ones. In general, scattered light will appear bluish, while the remaining directly transmitted light will lack the scattered blue rays and thus appear orange or red. Many natural blue tints are due to selective scattering rather than to blue pigments. The blue of skies and oceans is due to this kind of scattering. Blue eyes are the result of light scattering in the iris when a dark pigment is lacking.

Scattering by larger particles is nonselective and produces white. The whiteness of a bird's feather, of snow, and of clouds--all are due to scattering by particles which, though small, are large compared to the wavelength of light. [pg. 50]

Absorption of light as it passes through matter results in a decrease in intensity. Absorption, like scattering, may be general or selective. Selective absorption gives the world most of the colors we see. Glass filters which absorb part of the visible spectrum are used in research and photography. An absorption curve for a filter shows the amount of light absorbed at a particular wavelength. A unit thickness of the absorbing medium will always absorb the same fraction of light from a beam. If the first millimeter thickness of a filter absorbs 1/2 the light, the second millimeter absorbs 1/2 the remaining light, or 1/4 of the total. The third millimeter absorbs 1/2 of the 1/4, so only 1/8 of the light is transmitted through three millimeters of filter..... [p. 51]

Fluorescence and phosphorescence are caused by light striking atoms. In the collision, energy is transferred from the light to the electrons of the atoms. This energy may be re-radiated as light or dissipated as heat. If the emitted light is of the same frequency as the incident light, the effect is a kind of scattering. In many cases, however, the emitted light is of a different (usually lower) frequency than the incident light, and is characteristic of the atom that emitted it. The immediate re-radiation of absorbed light energy as light of a different color is called fluorescence. [The color of the fluorescence depends on the nature of the mineral.]

Some materials continue to emit light for a time after the incident radiation has been cut off. This is phosphorescence, usually a property of crystals or of large organic molecules. Phosphorescence often depends on the presence of minute quantities of impurities or imperfections in the crystal that provide "traps" for excited electrons. These electrons have received extra energy from incident radiation. The electrons remain in the "traps" until shaken loose by the heat vibrations of the atoms in the crystal. Phosphorescent light is emitted as the electrons return to their normal positions. Solid substances that produce light in this way are called phosphors. [p. 52]

Polarized light waves are restricted in their direction of vibration. Normal light waves vibrate in an infinite number of directions perpendicular to their direction of travel. For example, in the head-on view of unpolarized light the lines a, b, c, d, and an infinite number of others are perpendicular to the ray. At a particular instant any one of them might represent the direction of the vibrations. Thus, from moment to moment, the direction of the light vibrations changes in a random fashion. When components of vibration in one direction only are present, the light is plane polarized. [p. 53]

Plane of vibration of a polarized light wave is usually unaffected in passing through a transparent material--it remains polarized in the same plane. Some optically active materials, however, rotate the plane of vibration in either a clockwise or counterclockwise direction. Quartz crystals occur in both clockwise and counterclockwise varieties. Sugar solutions are also optically active. A chemist can determine the concentration of sugar in a solution by measuring the rotation of the plane of vibration when plane-polarized light is passed through the solution. A dextrose sugar solution causes a clockwise rotation; levulose sugar, a counterclockwise one. A device for measuring the angle of rotation of the plane of vibration is called a polariscope. A sacharimeter is a polariscope used in sugar analyses. [p. 54]

Doubly refracting crystals, such as calcite and quartz, break up light rays into two parts, called ordinary rays and extraordinary rays, which are polarized at right angles to each other. Such a crystal has a different refractive index for each of the two rays, and they are bent at different angles when they enter the crystal. This double refraction will form two images when a calcite crystal is placed over a dot on a piece of paper. The dot appears as two dots a small distance apart. Rotating the crystal causes one of the dots to rotate about the other. The dot that remains stationary is the image formed by the ordinary ray. This always lies in the plane of incidence (plane including the normal and the incident ray). The moving dot is the image formed by the extraordinary ray. [pg. 55]

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